Approximation of fixed points for enriched nonexpansive mappings in Banach spaces

Abstract

The three--step iteration scheme due to Thakur et al. [\emph{J. Inequal. Appl.} {\bf2014}, 328.] is analyzed with the new setting of mappings called enriched nonexpansive mappings. We establish weak convergence using the well-known Opial's condition and also prove strong convergence under various assumptions on the domain or on the mapping. Finally using an example of enriched nonexpansive mappings that is not nonexpansive, we show that the rate of convergence of the three-step Thakur iteration scheme is still more effective than the some other three-step iterative schemes of the literature. The presented outcome is essentially novel and extend the corresponding announced results of the literature.